load modular_matrix_divide.ijs open script for function/adverb definitions gcd's, gauss-jordan, modulo divide and modular matrix divide
I think this is a draft of the modular matrix system solver that I imagined a couple decades ago. It may still have some rough edges/mistakes. gcd2x 51 119 17 _2 1 _2 1 +/ . * 51 119 17 NB. more general than integer gcd2x 53r3 20 1r3 17 _15 NB. md is meant to be like % mod m 7 md 6 6 m md i.&.<:m=:7 1 4 5 2 3 6 m md i.&.<:m=:8 1 _ 3 _ 5 _ 7 5 m md i.&.<:m 5 _ 7 _ 1 _ 3 NB. Md is meant to be like %. mod m -/ . * a=:?.3 3$5 _7 a 4 1 3 1 0 3 1 1 1 ]ai=: 17 Md a 15 7 2 7 12 11 12 15 5 17|ai mp a 1 0 0 0 1 0 0 0 1 1 2 3 (17) Md a 1 13 6 NB. Non square case includes: NB. Can take an independent direction b and NB. make one, B, orthogonal to the columns of A -- NB. as in Gram-Schmidt even if not "least squares fit" $A=:a,1 4 3 17 Md A NB. Left inverse 15 7 1 1 7 12 14 14 12 15 11 11 17|(17 Md A)mp A 1 0 0 0 1 0 0 0 1 b=:1 2 3 4 s=:b 17 Md A 17| (B=:17|b-A mp s) mp A 0 0 0 B 0 0 8 9 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
